problem stringlengths 119 5.62k | prompt stringlengths 241 5.75k | completions listlengths 128 128 | scores listlengths 128 128 | predictions listlengths 128 128 | hidden_states_files listlengths 128 128 | prompt_ids listlengths 59 2.79k | completions_ids listlengths 128 128 | thoughts_len listlengths 128 128 | thoughts_ids_len listlengths 128 128 | step_rewards_vgs listlengths 128 128 | answer stringclasses 4
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
"Among the following exoplanets, which one has the highest density?\n\na) An Earth-mass and Earth-ra(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Among the following exoplanets, which one has the highest (...TRUNCATED) | ["Okay, so I have this question about exoplanets and their densities. Hmm, let me think. The questio(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | ["C","B","B","B",null,null,"B","B","",null,null,"A","A",null,null,null,"C",null,null,null,null,"B","(...TRUNCATED) | ["hidden_states_sample000000_completion00.npy","hidden_states_sample000000_completion01.npy","hidden(...TRUNCATED) | [151646,151644,33610,279,2701,505,93460,1415,11,892,825,702,279,8426,17457,1939,64,8,1527,9237,1448,(...TRUNCATED) | [[32313,11,773,358,614,419,3405,911,505,93460,1415,323,862,89716,13,88190,11,1077,752,1744,13,576,34(...TRUNCATED) | [25868,26474,22613,19913,64690,59545,22850,39547,61808,61601,66652,22249,30158,53133,65967,58232,220(...TRUNCATED) | [6585,6679,6001,4934,16384,16384,5870,10262,16384,16384,16384,5607,7684,16384,16384,16384,5463,16384(...TRUNCATED) | [[0.0009226073],[0.0008791795],[0.7190905213],[0.0724195838],[0.0000496845],[0.0000236975],[0.011159(...TRUNCATED) | D |
"Observations of structures located at a distance of about 2.1 gigaparsecs (2.1 Gpc) are being carri(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Observations of structures located at a distance of about (...TRUNCATED) | ["Okay, so I've got this question about observations in the Milky Way involving absorption lines. Hm(...TRUNCATED) | [0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,0.0(...TRUNCATED) | ["B","C","B","C","A","B","B","D",null,"D","C","B","B","A",null,null,"B","C","C","C","B","C","C","C",(...TRUNCATED) | ["hidden_states_sample000001_completion00.npy","hidden_states_sample000001_completion01.npy","hidden(...TRUNCATED) | [151646,151644,37763,804,315,14389,7407,518,264,6010,315,911,220,17,13,16,22583,391,2583,4837,320,17(...TRUNCATED) | [[32313,11,773,358,3003,2684,419,3405,911,23722,304,279,88719,12149,15860,43125,5128,13,88190,11,107(...TRUNCATED) | [8790,9270,19499,3691,10828,14184,14296,22143,25045,21470,13894,11472,38786,21703,44609,32252,15536,(...TRUNCATED) | [2153,2489,5159,939,2987,4023,4428,5528,8369,5986,3843,2929,10829,6255,16384,9080,4203,5752,8820,865(...TRUNCATED) | [[0.102765128],[0.9182816148],[0.0255359076],[0.9926393032],[0.4303683341],[0.272134155],[0.03488178(...TRUNCATED) | C |
"Astronomers are studying a system of three exoplanets (Planet1, Planet2, and Planet3) with circular(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Astronomers are studying a system of three exoplanets (Pla(...TRUNCATED) | ["Okay, so I've got this problem about three exoplanets, Planet1, Planet2, and Planet3. They all hav(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D","D"(...TRUNCATED) | ["hidden_states_sample000002_completion00.npy","hidden_states_sample000002_completion01.npy","hidden(...TRUNCATED) | [151646,151644,32,495,14274,388,525,20956,264,1849,315,2326,505,93460,1415,320,59634,16,11,28835,17,(...TRUNCATED) | [[32313,11,773,358,3003,2684,419,3491,911,2326,505,93460,1415,11,28835,16,11,28835,17,11,323,28835,1(...TRUNCATED) | [7830,10047,11557,11913,12021,10099,15336,9240,7879,10991,14097,8092,13657,10913,18788,14436,11277,1(...TRUNCATED) | [2642,3650,4161,3841,4670,3732,6049,3034,3195,3466,5129,3100,4521,4939,7739,5447,3615,4156,4022,2707(...TRUNCATED) | [[0.8817508221],[0.0954252779],[0.997361362],[0.9959706664],[0.1558373719],[0.7529891133],[0.9995786(...TRUNCATED) | D |
"Astronomers are studying a star with a 1.5 solar radius and 1.1 solar masses. When the star's surfa(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Astronomers are studying a star with a 1.5 solar radius an(...TRUNCATED) | ["Alright, let's tackle this problem step by step. It's about a star with some changes in its surfac(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | ["C","C","C","C","C","C","C","C","C","C","C","A","B",null,"C","C","C","C","C","C","C","C","C","C","C(...TRUNCATED) | ["hidden_states_sample000003_completion00.npy","hidden_states_sample000003_completion01.npy","hidden(...TRUNCATED) | [151646,151644,32,495,14274,388,525,20956,264,6774,448,264,220,16,13,20,12941,10578,323,220,16,13,16(...TRUNCATED) | [[71486,11,1077,594,21403,419,3491,3019,553,3019,13,1084,594,911,264,6774,448,1045,4344,304,1181,732(...TRUNCATED) | [8264,7692,10668,12065,39812,13641,12508,7119,8121,22745,13906,31825,14764,47852,9015,6341,17821,237(...TRUNCATED) | [3001,3010,3795,4415,13710,4932,6016,2691,3355,8465,5536,10759,5232,16384,3937,2662,6236,8505,3576,4(...TRUNCATED) | [[0.9708554745],[0.991078794],[0.9760860205],[0.9979834557],[0.5057256222],[0.7065475583],[0.9873664(...TRUNCATED) | C |
"Two planets have been detected orbiting a star using both the transit and radial velocity (RV) meth(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Two planets have been detected orbiting a star using both (...TRUNCATED) | ["Okay, so I've got this problem about two planets orbiting a star, and I need to find the ratio of (...TRUNCATED) | [1.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0(...TRUNCATED) | ["C","D","C","C",null,"D",null,null,"C",null,null,"D",null,"C","C","C","C","D",null,"C","C",null,"C"(...TRUNCATED) | ["hidden_states_sample000004_completion00.npy","hidden_states_sample000004_completion01.npy","hidden(...TRUNCATED) | [151646,151644,11613,32875,614,1012,16507,26507,287,264,6774,1667,2176,279,24065,323,56836,15435,320(...TRUNCATED) | [[32313,11,773,358,3003,2684,419,3491,911,1378,32875,26507,287,264,6774,11,323,358,1184,311,1477,279(...TRUNCATED) | [11989,38107,39918,20291,47001,37032,41625,43312,16501,45308,36812,25544,44915,20344,14816,30987,175(...TRUNCATED) | [4947,12614,13968,6894,16384,12727,16383,16384,6285,16384,16384,9207,16384,7717,5569,10582,7245,1632(...TRUNCATED) | [[0.1215272844],[0.1939552724],[0.7541780472],[0.2251863033],[0.0000443744],[0.1185767427],[0.000039(...TRUNCATED) | C |
"Astronomers are currently observing a star with a radius equal to that of the Sun. One hemisphere (...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Astronomers are currently observing a star with a radius e(...TRUNCATED) | ["Okay, so I have this problem about a star with dark spots and an exoplanet that could cause a simi(...TRUNCATED) | [1.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,1.0,0.0(...TRUNCATED) | ["A","A",null,null,null,null,"B","A","B",null,"A","D","A","D","A",null,null,null,"A","A",null,null,n(...TRUNCATED) | ["hidden_states_sample000005_completion00.npy","hidden_states_sample000005_completion01.npy","hidden(...TRUNCATED) | [151646,151644,32,495,14274,388,525,5023,44971,264,6774,448,264,10578,6144,311,429,315,279,8059,13,3(...TRUNCATED) | [[32313,11,773,358,614,419,3491,911,264,6774,448,6319,18773,323,458,505,93460,295,429,1410,5240,264,(...TRUNCATED) | [12150,16497,47904,48358,47390,42600,24192,11124,44350,50363,26287,28677,16187,42880,23945,48276,557(...TRUNCATED) | [3106,5204,16384,16384,16384,16384,7368,3851,16284,16384,8599,10889,4761,15219,8689,16384,16384,1638(...TRUNCATED) | [[0.640340209],[0.9491221309],[0.0000755731],[0.0002091843],[0.0000884359],[0.0004352215],[0.9692144(...TRUNCATED) | A |
"Which of the following stars can be detected with both the ESPRESSO spectrograph at the Paranal Obs(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Which of the following stars can be detected with both the(...TRUNCATED) | ["Alright, so I've got this question about which stars can be detected by both ESPRESSO at Paranal O(...TRUNCATED) | [0.0,1.0,0.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0(...TRUNCATED) | ["A","C","D","B","D","C","C",null,"B","B","A",null,"A","C",null,"A",null,"C","A",null,null,null,"B",(...TRUNCATED) | ["hidden_states_sample000006_completion00.npy","hidden_states_sample000006_completion01.npy","hidden(...TRUNCATED) | [151646,151644,23085,315,279,2701,9759,646,387,16507,448,2176,279,18117,7817,46,65325,4439,518,279,4(...TRUNCATED) | [[71486,11,773,358,3003,2684,419,3405,911,892,9759,646,387,16507,553,2176,18117,7817,46,518,4270,488(...TRUNCATED) | [32207,17672,44066,46548,42447,37974,39073,56291,29531,40344,40289,41100,39486,12285,52106,7628,4563(...TRUNCATED) | [9307,5491,13137,15508,12847,11300,12414,16384,8537,12640,12333,12539,12180,3820,16384,2862,13454,10(...TRUNCATED) | [[0.032977771],[0.0225526132],[0.0444150902],[0.0012755076],[0.0104021691],[0.0047737621],[0.0009406(...TRUNCATED) | C |
"Observations of a quasar across the electromagnetic spectrum are being carried out. Focusing on the(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Observations of a quasar across the electromagnetic spectr(...TRUNCATED) | ["Okay, so I need to figure out the comoving distance to a quasar based on the given spectral observ(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | ["B",null,"C",null,"B","D","A","A","C","A","C","D","B","A","C","B","B",null,null,"D","B","B","B","C"(...TRUNCATED) | ["hidden_states_sample000007_completion00.npy","hidden_states_sample000007_completion01.npy","hidden(...TRUNCATED) | [151646,151644,37763,804,315,264,922,66938,3941,279,65569,19745,525,1660,11691,700,13,434,86495,389,(...TRUNCATED) | [[32313,11,773,358,1184,311,7071,700,279,469,9130,6010,311,264,922,66938,3118,389,279,2661,55977,237(...TRUNCATED) | [29935,26257,28751,37315,32173,29484,35652,39085,24546,43229,33035,24426,34068,40605,29167,22954,392(...TRUNCATED) | [10151,9964,11106,11367,14206,9215,14325,16030,9250,16360,13257,9053,10280,15021,9768,6824,12759,117(...TRUNCATED) | [[0.0837756917],[0.0557086505],[0.587518692],[0.0214848742],[0.0042033968],[0.0002362568],[0.0269074(...TRUNCATED) | A |
"Astronomers are studying two binary star systems: system_1 and system_2. Observations reveal that b(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Astronomers are studying two binary star systems: system_1(...TRUNCATED) | ["Okay, so I have this problem about two binary star systems, system_1 and system_2. Both systems ex(...TRUNCATED) | [0.0,1.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0(...TRUNCATED) | ["C","D","C","D",null,"D","D","B","D","D","D","D",null,"D","A","D","D","C","D","D","D","D","A","C","(...TRUNCATED) | ["hidden_states_sample000008_completion00.npy","hidden_states_sample000008_completion01.npy","hidden(...TRUNCATED) | [151646,151644,32,495,14274,388,525,20956,1378,7868,6774,5942,25,1849,62,16,323,1849,62,17,13,30843,(...TRUNCATED) | [[32313,11,773,358,614,419,3491,911,1378,7868,6774,5942,11,1849,62,16,323,1849,62,17,13,11733,5942,3(...TRUNCATED) | [18677,22073,26945,31046,35238,15309,12277,24106,17567,6394,27296,15743,35775,16350,22193,14100,1261(...TRUNCATED) | [6444,8995,10679,13750,16384,5357,4079,11258,7489,2334,12470,6467,16384,7405,8992,5490,4984,4031,141(...TRUNCATED) | [[0.0100784497],[0.0034471883],[0.0582508035],[0.2850228846],[0.000023968],[0.0018689025],[0.0150807(...TRUNCATED) | D |
"Very large number of neutrinos produced by the Sun reach the Earth (very large flux of neutrinos, d(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>Very large number of neutrinos produced by the Sun reach t(...TRUNCATED) | ["Alright, so I need to figure out the approximate ratio of the neutrino flux between two energy ban(...TRUNCATED) | [0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | ["C","A",null,"C","B","C","C","A","D",null,"C","C","D","A","C","C","C","C",null,"C","C","C","C","D",(...TRUNCATED) | ["hidden_states_sample000009_completion00.npy","hidden_states_sample000009_completion01.npy","hidden(...TRUNCATED) | [151646,151644,25756,3460,1372,315,41599,15215,8947,553,279,8059,5545,279,9237,320,1204,3460,30305,3(...TRUNCATED) | [[71486,11,773,358,1184,311,7071,700,279,44868,11341,315,279,41599,3313,30305,1948,1378,4802,20892,2(...TRUNCATED) | [20807,25808,28810,34650,38472,31964,29505,46400,27934,40372,29762,26560,34315,27947,38572,23398,296(...TRUNCATED) | [5474,7322,8154,10447,11606,9402,8337,12785,6784,16384,9202,6733,10008,7309,11950,6024,8951,8381,106(...TRUNCATED) | [[0.0000347052],[0.099030599],[0.0008598883],[0.0566830859],[0.0035269875],[0.000052137],[0.00002138(...TRUNCATED) | B |
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